Multiplicity codes are a generalization of RS and RM codes where for each evaluation point we output the evaluation of a low-degree polynomial and all of its directional derivatives up to order $s$. Multi-variate multiplicity codes are locally decodable with the natural local decoding algorithm that reads values on a ... more >>>

We construct a family of binary codes of relative distance $\frac{1}{2}-\varepsilon$ and rate $\varepsilon^{2} \cdot 2^{-\log^{\alpha}(1/\varepsilon)}$ for $\alpha \approx \frac{1}{2}$ that are decodable, probabilistically, in near linear time. This improves upon the rate of the state-of-the-art near-linear time decoding near the GV bound due to Jeronimo, Srivastava, and Tulsiani, who ... more >>>

An $m$-catalytic branching program (Girard, Koucky, McKenzie 2015) is a set of $m$ distinct branching programs for $f$ which are permitted to share internal (i.e. non-source non-sink) nodes. While originally introduced as a non-uniform analogue to catalytic space, this also gives a natural notion of amortized non-uniform space complexity for ... more >>>